7x^2-14x-196=-8

Solution for 7x^2-14x-196=-8 equation:

7x^2-14x-196=-8

We move all terms to the left:

7x^2-14x-196-(-8)=0

We add all the numbers together, and all the variables

7x^2-14x-188=0

a = 7; b = -14; c = -188;
Δ = b2-4ac
Δ = -142-4·7·(-188)
Δ = 5460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5460}=\sqrt{4*1365}=\sqrt{4}*\sqrt{1365}=2\sqrt{1365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{1365}}{2*7}=\frac{14-2\sqrt{1365}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{1365}}{2*7}=\frac{14+2\sqrt{1365}}{14}
$